A projectile is known and described in German published Patent Application No. DE-OS 25 57 676 which projectile body has a casing which is made up of a plurality of projectile heavy metal splinters, for example depleted uranium. Such a projectile made of steel, is for example, disclosed in Rheinmetall Taschenbuch, 1980 Edition, pg. 471, FIG. 1106. A casing made of heavy metal splinters is described in German published application DE-OS 255 7676. The splinters are embedded in a carrier substance of the casing and cause in addition to a pyrophoric effect at impacting of the splinters on a combustible substance also the mechanical effect of the uranium which is also useful at impact. Such a projectile is fabricated with a complex and costly manufacturing process. The casing consists of an inner and outer tubular body of the same material, whereby the projectile splinters, which are embedded in the carrier material, consist of a material having a substantially higher density. In order to give such a projectile a sufficient firing strength it is necessary for the projectile body to have a sufficiently wide cross-section. However, this makes it impossible to substantially increase the average specific weight of the projectile casing. It has been found to be particularly disadvantageous in this known projectile that the amount of projectile splinters, consisting of an effective depleted uranium embedded into the carrier substance, is limited as a result of having to maintain a sufficient minimum firing strength. Consequently, the effect of the projectile and the splinters on the target becomes inadequate, in particular a full caliber explosive and incendiary projectile of less than 40 mm caliber because such projectile can only be maintained either by using dimensionally small embedded splinters or by a projectile casing being too thick. At detonation there form, preponderantly by the inner and outer cylindrical bodies of the projectile, projectile splinters of a reduced penetration capability, whereby the lighter produced splinters of the projectile casing can, on the one hand, not achieve a pyrophoric (incendiary) effect and, on the other hand, the incendiary effect on the target is significantly reduced.